The simple answer is that Henry wanted to write, and needed a quieter place
than the Thoreau household to do this. And he did write both A Week
on the Concord and Merrimack Rivers and an early draft of Walden
in his two years at the pond. But in Walden's "Where
I Lived, & What I Lived for," he describes an additional motive...

"I went to the woods because I wished to live deliberately,
to front only the essential facts of life, and see if I could not learn
what it had to teach, and not, when I came to die, discover that I had
not lived."

Thoreau wanted to get the most from his life by determining what was really
important, and he did that by removing himself somewhat from the normal
life of Concord, Massachusetts in the 1840's. One side of this was economic:
he reduced his material needs by living simply, so that he would not have
to spend much time supporting a lifestyle that he did not need or care
about. The other side was spiritual, not unlike the spiritual retreats
of eastern and western religions.